Interpretable and Efficient Data-driven Discovery and Control of Distributed Systems

• URL: http://arxiv.org/abs/2411.04098v1
• Date: Wed, 06 Nov 2024 18:26:19 GMT
• Title: Interpretable and Efficient Data-driven Discovery and Control of Distributed Systems
• Authors: Florian Wolf, Nicolò Botteghi, Urban Fasel, Andrea Manzoni,
• Abstract summary: Reinforcement Learning (RL) has emerged as a promising control paradigm for systems with high-dimensional, nonlinear dynamics. We propose a data-efficient, interpretable, and scalable framework for PDE control.
• Score: 1.5195865840919498
• License:
• Abstract: Effectively controlling systems governed by Partial Differential Equations (PDEs) is crucial in several fields of Applied Sciences and Engineering. These systems usually yield significant challenges to conventional control schemes due to their nonlinear dynamics, partial observability, high-dimensionality once discretized, distributed nature, and the requirement for low-latency feedback control. Reinforcement Learning (RL), particularly Deep RL (DRL), has recently emerged as a promising control paradigm for such systems, demonstrating exceptional capabilities in managing high-dimensional, nonlinear dynamics. However, DRL faces challenges including sample inefficiency, robustness issues, and an overall lack of interpretability. To address these issues, we propose a data-efficient, interpretable, and scalable Dyna-style Model-Based RL framework for PDE control, combining the Sparse Identification of Nonlinear Dynamics with Control (SINDy-C) algorithm and an autoencoder (AE) framework for the sake of dimensionality reduction of PDE states and actions. This novel approach enables fast rollouts, reducing the need for extensive environment interactions, and provides an interpretable latent space representation of the PDE forward dynamics. We validate our method on two PDE problems describing fluid flows - namely, the 1D Burgers equation and 2D Navier-Stokes equations - comparing it against a model-free baseline, and carrying out an extensive analysis of the learned dynamics.

Related papers

• Latent feedback control of distributed systems in multiple scenarios through deep learning-based reduced order models [3.5161229331588095]
  Continuous monitoring and real-time control of high-dimensional distributed systems are crucial in applications to ensure a desired physical behavior. Traditional feedback control design that relies on full-order models fails to meet these requirements due to the delay in the control computation. We propose a real-time closed-loop control strategy enhanced by nonlinear non-intrusive Deep Learning-based Reduced Order Models (DL-ROMs)
  arXiv  Detail & Related papers  (2024-12-13T08:04:21Z)
• Wavelet Diffusion Neural Operator [17.617919636212445]
  We propose Wavelet Neural Diffusion Operator (WDNO), a novel PDE simulation and control framework. WDNO performs diffusion-based generative modeling in the wavelet domain to handle abrupt changes and long-term dependencies effectively. To address the issue of poor generalization across different resolutions, we introduce multi-resolution training.
  arXiv  Detail & Related papers  (2024-12-06T07:56:25Z)
• Advancing Generalization in PINNs through Latent-Space Representations [71.86401914779019]
  Physics-informed neural networks (PINNs) have made significant strides in modeling dynamical systems governed by partial differential equations (PDEs) We propose PIDO, a novel physics-informed neural PDE solver designed to generalize effectively across diverse PDE configurations. We validate PIDO on a range of benchmarks, including 1D combined equations and 2D Navier-Stokes equations.
  arXiv  Detail & Related papers  (2024-11-28T13:16:20Z)
• Learning Controlled Stochastic Differential Equations [61.82896036131116]
  This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion. We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity. Our method is available as an open-source Python library.
  arXiv  Detail & Related papers  (2024-11-04T11:09:58Z)
• SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning [5.59265003686955]
  We introduce SINDy-RL, a framework for combining SINDy and deep reinforcement learning. SINDy-RL achieves comparable performance to state-of-the-art DRL algorithms. We demonstrate the effectiveness of our approaches on benchmark control environments and challenging fluids problems.
  arXiv  Detail & Related papers  (2024-03-14T05:17:39Z)
• Physics-constrained robust learning of open-form partial differential equations from limited and noisy data [1.50528618730365]
  This study proposes a framework to robustly uncover open-form partial differential equations (PDEs) from limited and noisy data. A neural network-based predictive model fits the system response and serves as the reward evaluator for the generated PDEs. Numerical experiments demonstrate our framework's capability to uncover governing equations from nonlinear dynamic systems with limited and highly noisy data.
  arXiv  Detail & Related papers  (2023-09-14T12:34:42Z)
• Solving High-Dimensional PDEs with Latent Spectral Models [74.1011309005488]
  We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space. LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks.
  arXiv  Detail & Related papers  (2023-01-30T04:58:40Z)
• Capturing Actionable Dynamics with Structured Latent Ordinary Differential Equations [68.62843292346813]
  We propose a structured latent ODE model that captures system input variations within its latent representation. Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
  arXiv  Detail & Related papers  (2022-02-25T20:00:56Z)
• DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization [77.34726150561087]
  We introduce Discovery of Dynamical Systems via Moving Horizon Optimization (DySMHO), a scalable machine learning framework. DySMHO sequentially learns the underlying governing equations from a large dictionary of basis functions. Canonical nonlinear dynamical system examples are used to demonstrate that DySMHO can accurately recover the governing laws.
  arXiv  Detail & Related papers  (2021-07-30T20:35:03Z)
• Learning to Control PDEs with Differentiable Physics [102.36050646250871]
  We present a novel hierarchical predictor-corrector scheme which enables neural networks to learn to understand and control complex nonlinear physical systems over long time frames. We demonstrate that our method successfully develops an understanding of complex physical systems and learns to control them for tasks involving PDEs.
  arXiv  Detail & Related papers  (2020-01-21T11:58:41Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.